# Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals

arXiv: https://arxiv.org/abs/1311.2150 · HTML: https://mlsanity.com/paper/1311.2150/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2013.

## Built on by (most cited first, 10 of 10)

- [Covariance-Free Sparse Bayesian Learning](https://mlsanity.com/paper/2105.10439/) (2021)
- [High-Dimensional Sparse Bayesian Learning without Covariance Matrices](https://mlsanity.com/paper/2202.12808/) (2022)
- [Block Sparse Bayesian Learning: A Diversified Scheme](https://mlsanity.com/paper/2402.04646/) (2024)
- [Adaptive Block Sparse Regularization under Arbitrary Linear Transform](https://mlsanity.com/paper/2401.15292/) (2024)
- [Spectral Unmixing of Hyperspectral Images Based on Block Sparse Structure](https://mlsanity.com/paper/2204.04638/) (2022)
- [A Sparse Bayesian Learning for Diagnosis of Nonstationary and Spatially Correlated Faults with Application to Multistation Assembly Systems](https://mlsanity.com/paper/2310.16058/) (2023)
- [SPP-SBL: Space-Power Prior Sparse Bayesian Learning for Block Sparse Recovery](https://mlsanity.com/paper/2505.08518/) (2025)
- [Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties](https://mlsanity.com/paper/2603.01304/) (2026)
- [Deep Unfolded Latent Optimally Partitioned-l2/l1 Networks for Data-driven Block-Sparse Recovery](https://mlsanity.com/paper/2606.12740/) (2026)
- [Hybrid-Field Sparse Channel Representation and Recovery for XL-RIS-Assisted mmWave MIMO Systems](https://mlsanity.com/paper/2608.00052/) (2026)

## Abstract (arXiv)

We consider the problem of recovering block-sparse signals whose structures are unknown a priori. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. Specifically, a pattern-coupled hierarchical Gaussian prior model is introduced to characterize the statistical dependencies among coefficients, in which a set of hyperparameters are employed to control the sparsity of signal coefficients. Unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters of its immediate neighbors. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters, along with the sparse signal, are learned by maximizing their posterior probability via an expectation-maximization (EM) algorithm. Numerical results show that the proposed algorithm presents uniform superiority over other existing methods in a series of experiments.